Artin representation data - 1.75.10t1.a

Formats: - HTML - YAML - JSON - 2025-05-26T03:25:13.040697

• artin_reps •

  Column	Type
  BadPrimes	jsonb
  Baselabel	text
  CharacterField	smallint
  Conductor	numeric
  Container	text
  Dets	text[]
  Dim	smallint
  GalConjSigns	jsonb
  Galn	smallint
  GaloisConjugates	jsonb
  GaloisConjugatesSigns	integer[]
  GaloisLabel	text
  Galt	integer
  HardPrimes	jsonb
  Hide	smallint
  Indicator	smallint
  Is_Even	boolean
  NFGal	jsonb
  NumBadPrimes	smallint
  Proj_GAP	integer[]
  Proj_Polynomial	numeric[]
  Proj_nTj	integer[]

  
  {'BadPrimes': [3, 5], 'Baselabel': '1.75.10t1.a', 'CharacterField': 5, 'Conductor': 75, 'Container': '10t1', 'Dets': ['75.11', '75.41', '75.56', '75.71'], 'Dim': 1, 'GalConjSigns': [0, 0, 0, 0], 'Galn': 10, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [-1], [-1, -1, -1, -1], [0, 0, 0, 1], [0, 0, 1], [0, 1], [0, 0, -1], [0, -1], [1, 1, 1, 1], [0, 0, 0, -1]], 'GalOrbIndex': 1, 'HardFactors': [9, 11, 11, 1, 5, 1, 1], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [1, 1, 1, 1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, -1]], [[1], [0, -1]], [[1], [0, 0, 1]], [[1], [0, 1]], [[1], [-1, -1, -1, -1]], [[1], [0, 0, 0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [-1, -1, -1, -1], [0, 0, 0, -1], [1, 1, 1, 1], [0, -1], [0, 0, -1]], 'GalOrbIndex': 2, 'HardFactors': [9, 11, 11, 1, 5, 1, 1], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, -1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, -1]], [[1], [1, 1, 1, 1]], [[1], [0, 0, 0, 1]], [[1], [-1, -1, -1, -1]], [[1], [0, 1]], [[1], [0, 0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, 0, 1], [-1, -1, -1, -1], [0, 1], [0, 0, 0, 1], [0, -1], [0, 0, 0, -1], [0, 0, -1], [1, 1, 1, 1]], 'GalOrbIndex': 3, 'HardFactors': [9, 11, 11, 1, 5, 1, 1], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, -1]], [[1], [1, 1, 1, 1]], [[1], [0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, 1]], [[1], [0, 0, 0, 1]], [[1], [0, 0, 1]], [[1], [-1, -1, -1, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, 0, 0, 1], [0, 1], [-1, -1, -1, -1], [0, 0, 1], [1, 1, 1, 1], [0, 0, -1], [0, 0, 0, -1], [0, -1]], 'GalOrbIndex': 4, 'HardFactors': [9, 11, 11, 1, 5, 1, 1], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, 0, -1]], [[1], [0, -1]], [[1], [1, 1, 1, 1]], [[1], [0, 0, -1]], [[1], [-1, -1, -1, -1]], [[1], [0, 0, 1]], [[1], [0, 0, 0, 1]], [[1], [0, 1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0, 0, 0], 'GaloisLabel': '10T1', 'Galt': 1, 'HardPrimes': [2, 3, 5, 7, 31, 157, 199], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [1, 10, 95, 70, 125, -49, 90, -10, 10, 0, 1], 'NumBadPrimes': 2, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
• artin_field_data •

  Column	Type
  ArtinReps	jsonb
  ComplexConjugation	smallint
  ConjClasses	jsonb
  FrobResolvents	jsonb
  Frobs	jsonb
  G-Gens	jsonb
  G-Name	text
  Polynomial	jsonb
  QpRts	jsonb
  QpRts-minpoly	jsonb
  QpRts-p	integer
  QpRts-prec	integer
  Size	numeric
  TransitiveDegree	smallint

  
  {'ArtinReps': [{'GalConj': 1, 'Baselabel': '1.1.1t1.a', 'Character': [[1], [1], [1], [1], [1], [1], [1], [1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.3.2t1.a', 'Character': [[1], [-1], [1], [1], [1], [1], [-1], [-1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 3, 'Baselabel': '1.25.5t1.a', 'Character': [[1, 0, 0, 0], [1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1], [-1, -1, -1, -1], [0, 0, 0, 1], [-1, -1, -1, -1], [0, 1, 0, 0], [0, 0, 1, 0]], 'CharacterField': 5}, {'GalConj': 2, 'Baselabel': '1.75.10t1.a', 'Character': [[1, 0, 0, 0], [-1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1], [-1, -1, -1, -1], [0, 0, 0, -1], [1, 1, 1, 1], [0, -1, 0, 0], [0, 0, -1, 0]], 'CharacterField': 5}, {'GalConj': 1, 'Baselabel': '1.25.5t1.a', 'Character': [[1, 0, 0, 0], [1, 0, 0, 0], [0, 0, 1, 0], [-1, -1, -1, -1], [0, 1, 0, 0], [0, 0, 0, 1], [0, 1, 0, 0], [0, 0, 0, 1], [0, 0, 1, 0], [-1, -1, -1, -1]], 'CharacterField': 5}, {'GalConj': 3, 'Baselabel': '1.75.10t1.a', 'Character': [[1, 0, 0, 0], [-1, 0, 0, 0], [0, 0, 1, 0], [-1, -1, -1, -1], [0, 1, 0, 0], [0, 0, 0, 1], [0, -1, 0, 0], [0, 0, 0, -1], [0, 0, -1, 0], [1, 1, 1, 1]], 'CharacterField': 5}, {'GalConj': 4, 'Baselabel': '1.25.5t1.a', 'Character': [[1, 0, 0, 0], [1, 0, 0, 0], [0, 0, 0, 1], [0, 1, 0, 0], [-1, -1, -1, -1], [0, 0, 1, 0], [-1, -1, -1, -1], [0, 0, 1, 0], [0, 0, 0, 1], [0, 1, 0, 0]], 'CharacterField': 5}, {'GalConj': 4, 'Baselabel': '1.75.10t1.a', 'Character': [[1, 0, 0, 0], [-1, 0, 0, 0], [0, 0, 0, 1], [0, 1, 0, 0], [-1, -1, -1, -1], [0, 0, 1, 0], [1, 1, 1, 1], [0, 0, -1, 0], [0, 0, 0, -1], [0, -1, 0, 0]], 'CharacterField': 5}, {'GalConj': 2, 'Baselabel': '1.25.5t1.a', 'Character': [[1, 0, 0, 0], [1, 0, 0, 0], [-1, -1, -1, -1], [0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 1, 0, 0], [-1, -1, -1, -1], [0, 0, 0, 1]], 'CharacterField': 5}, {'GalConj': 1, 'Baselabel': '1.75.10t1.a', 'Character': [[1, 0, 0, 0], [-1, 0, 0, 0], [-1, -1, -1, -1], [0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0], [0, 0, -1, 0], [0, -1, 0, 0], [1, 1, 1, 1], [0, 0, 0, -1]], 'CharacterField': 5}], 'ComplexConjugation': 2, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]}, {'Size': '1', 'Order': 2, 'Representative': [5, 7, 10, 8, 1, 9, 2, 4, 6, 3]}, {'Size': '1', 'Order': 5, 'Representative': [10, 1, 9, 2, 3, 4, 5, 7, 8, 6]}, {'Size': '1', 'Order': 5, 'Representative': [6, 10, 8, 1, 9, 2, 3, 5, 7, 4]}, {'Size': '1', 'Order': 5, 'Representative': [4, 6, 7, 10, 8, 1, 9, 3, 5, 2]}, {'Size': '1', 'Order': 5, 'Representative': [2, 4, 5, 6, 7, 10, 8, 9, 3, 1]}, {'Size': '1', 'Order': 10, 'Representative': [8, 9, 2, 3, 4, 5, 6, 10, 1, 7]}, {'Size': '1', 'Order': 10, 'Representative': [7, 8, 1, 9, 2, 3, 4, 6, 10, 5]}, {'Size': '1', 'Order': 10, 'Representative': [3, 5, 6, 7, 10, 8, 1, 2, 4, 9]}, {'Size': '1', 'Order': 10, 'Representative': [9, 3, 4, 5, 6, 7, 10, 1, 2, 8]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': 0, 'Classes': 2, 'Algorithm': 'CYC', 'CycleType': [2, 2, 2, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [-5, 11, -7, 1]}, 'Classes': [{'RootOf': ['-260', '1'], 'ConjugacyClass': 3}, {'RootOf': ['115', '1'], 'ConjugacyClass': 4}, {'RootOf': ['-610', '1'], 'ConjugacyClass': 5}, {'RootOf': ['165', '1'], 'ConjugacyClass': 6}], 'Algorithm': 'RES', 'CycleType': [5, 5]}, {'Data': {'Powers': [1], 'Resolvent': [-5, 11, -7, 1]}, 'Classes': [{'RootOf': ['290', '1'], 'ConjugacyClass': 7}, {'RootOf': ['15', '1'], 'ConjugacyClass': 8}, {'RootOf': ['115', '1'], 'ConjugacyClass': 9}, {'RootOf': ['-35', '1'], 'ConjugacyClass': 10}], 'Algorithm': 'RES', 'CycleType': [10]}], 'Frobs': [9, 4, 2, 1, 9, 6, 7, 5, 9, 10, 5, 6, 8, 1, 10, 10, 8, 3, 5, 10, 3, 4, 7, 9, 4, 2, 4, 2, 6, 8, 3, 7, 8, 3, 2, 1, 1, 6, 7, 9, 10, 5, 8, 1, 10, 1, 3, 3, 9, 4, 7, 9, 6, 2, 2, 8, 7, 4, 3, 7, 5, 2, 1, 9, 6, 7, 5, 6, 10, 1, 10, 8, 5, 3, 4, 7, 9, 4, 2, 6, 7, 4, 7, 5, 3, 2, 2, 1, 9, 6, 7, 10, 6, 8, 1, 10, 8, 10, 3, 6, 4, 2, 8, 7, 4, 3, 8, 2, 2, 1, 1, 6, 7, 5, 5, 8, 1, 10, 10, 8, 3, 3, 9, 7, 6, 2, 6, 7, 3, 5, 3, 2, 1, 1, 9, 5, 9, 6, 10, 8, 3, 10, 3, 9, 4, 9, 4, 2, 6, 8, 3, 7, 5, 8, 1, 9, 5, 10, 6, 8, 10, 10, 5, 10, 9, 7, 6, 4], 'G-Gens': [[5, 7, 10, 8, 1, 9, 2, 4, 6, 3], [8, 9, 2, 3, 4, 5, 6, 10, 1, 7]], 'G-Name': 'C10', 'Polynomial': [1, 10, 95, 70, 125, -49, 90, -10, 10, 0, 1], 'QpRts': [['-736196', '-548425', '-583467', '1199572', '976641'], ['1152070', '274338', '200464', '-626130', '963373'], ['1288536', '-1116037', '-644610', '-1677585', '-2010737'], ['-2005520', '-2280525', '70125', '-56712', '-626725'], ['10707', '-1571747', '882476', '1351770', '-2108383'], ['1765674', '-664851', '-1050998', '1895043', '-51578'], ['-1283993', '-1385283', '1130427', '-2335587', '1107130'], ['35252', '767650', '805177', '528328', '-1195686'], ['-50502', '-1521392', '-2173470', '2133074', '-619133'], ['-176028', '-1607346', '1363876', '-2411773', '-1261711']], 'QpRts-minpoly': [11, 4, 0, 0, 0, 1], 'QpRts-p': 13, 'QpRts-prec': 6, 'Size': 10, 'TransitiveDegree': 10}